Donagi-Witten construction and a graded covering of a supermanifold

Abstract: In the paper "Super Atiyah classes and obstructions to splitting of supermoduli space", Donagi and Witten suggested a construction of a first obstruction class for splitting of a supermanifold via differential operators. We generalize this idea. As a result we obtain a family of embeddings of the category of supermanifolds into the category of iterated vector bundles and into the category of graded manifolds. It was shown that the images of a supermanifold in these categories satisfy universal properties of a graded covering or a graded semicovering. In our talk we will discuss these functors in the case of a Lie supergroup and a Lie superalgebra. (Joint work with M. Rotkiewicz).

algebraic geometry

Audience: researchers in the topic

Brazilian algebraic geometry seminar

Series comments: Subscribe the seminar mailing list, please send and email to brag-seminar-request@lists.ime.unicamp.br with "subscribe" in the subject line.

Previous talks available at the YouTube channel "Brazilian Algebraic Geometry" www.youtube.com/channel/UCM-pcdNdpWxQFgOg-illE2w